created at May 22, 2021

Air resistance force

When body moves through a viscous fluid (air, water, etc.), the fluid acts on the body with some resistance force trying to stop the body. This is also called a drag force. Of coarse, the direction of force vector is the opposite to the body velocity vector.

Despite the fluid flow is a process quite difficult to understand and calculate, the drag force equation is simple:

F_{d}=C_{d}\cdot A\cdot \frac{\rho \cdot V^{2}}{2}

where:

Cd - the drag coefficient, which depends on the shape of the body
A - the cross sectional area
ρ - air density
V - velocity of the body (relative to the fluid)

The drag coefficient C_d depends on the shape of the body, it is dimensionless and is typically obtained through the experiments. You can find the values in the handbooks for the different shapes. Examples are:

Sphere	0.5
Cube	0.8
Squared flat plate (90°)	1.2
flat plate along turbulent flow	0.005
typical saloon car	0.3
Bicycle	0.9
Airplane wing at normal position	0.05

In general, the drag coefficient C_d is not a constant, and depends on Reynolds number. For some very low velocities as well as very high supersonic velocities it will be different, but for the most practical cases (for subsonic flow) it may be assumed as a constant.

The cross sectional area A is typically the maximum area frontal to the motion direction. In other words, if you project your body shape to the plane, which is orthogonal to the motion direction - the are of the shape you will obtain is the one you need. For the sphere it is π*D²/4. There are some exclusions though. For the airplane wing you should use the wing's area in the base plane.

The air is considered as example for this case, but you can calculate the drag force for any other fluid, just put appropriate value for density ρ. To calculate the drag force in the water, use ρ = 1000 kg/m³.